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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 149, Number 2, Pages 147–160
DOI: https://doi.org/10.4213/tmf4224 (Mi tmf4224) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Pairs of commuting Hamiltonians quadratic in the momenta

V. G. Marikhin, V. V. Sokolov

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Full-text PDF (417 kB) Citations (12)
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DOI: https://doi.org/10.4213/tmf4224
Abstract: In the case of two degrees of freedom, we consider pairs of Hamiltonians quadratic in the momenta and commuting with respect to the standard Poisson bracket. We find new multiparameter families of such pairs and present a universal scheme for constructing a complete solution of the Hamilton–Jacobi equation in terms of integrals over an algebraic curve. For the most complicated examples, this curve is a nonhyperelliptic covering of an elliptic curve.
Keywords: integrable Hamiltonian system, separation of variables, algebraic system.
Received: 24.05.2006
English version:
Theoretical and Mathematical Physics, 2006, Volume 149, Issue 2, Pages 1425–1436
DOI: https://doi.org/10.1007/s11232-006-0129-y
Bibliographic databases:
Language: Russian
Citation: V. G. Marikhin, V. V. Sokolov, “Pairs of commuting Hamiltonians quadratic in the momenta”, TMF, 149:2 (2006), 147–160; Theoret. and Math. Phys., 149:2 (2006), 1425–1436
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v149/i2/p147
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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